Attractive step-step interactions, tricriticality, and faceting in the orientational phase diagram of silicon surfaces between [113] and [114]

A synchrotron x-ray scattering study is presented of the orientational phase diagram of Si surfaces misoriented by up to 6^∘{} from the cubic [113] direction towards [001] and for temperatures between 300 and 1500 K. At the highest temperatures (above 1223 K), the surface is uniformly stepped. In this region, the intensity of near-specularly scattered x rays increases with decreasing temperature, suggesting a corresponding increase in the surface roughness. Specifically, the temperature dependence of the intensity of the near-specular diffuse scattering may be described as a power law versus reduced temperature: ID{~}tₛ^-λ, with {λ}=0.76±{}0.2 (tₛ({θ})=[T-Tₛ({θ})]/Tₛ({θ}), where Tₛ({θ}) is spinodal temperature for surface misorientation {θ}). Below Tₜ=1223±{}40 K, there is a two-phase region in which (113) facets appear in coexistence with the stepped phase. We identify Tₜ as a tricritical point. The misorientation angle at the phase boundary separating one- and two-phase regions may be also described as a power law versus reduced temperature: {θ}=θ₀{t}^{{{β}}}, with β=0.42±0.10 [t=({T}ₜ$-T)/${T}ₜ$]. The behavior of the intensity of the diffuse scattering above ${T}ₜ$ and of the phase boundary below ${T}ₜ$ can be understood qualitatively on the basis of a mean-field theory incorporating a direct attractive interaction between steps. However, the observed tricritical exponents are not given correctly. For temperatures between a triple point at T₃=1134±{}40 and 300 K, coexistence between the (113) facet and the (114) facet is found.